2x^2-16x+22=0

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Solution for 2x^2-16x+22=0 equation:


Simplifying
2x2 + -16x + 22 = 0

Reorder the terms:
22 + -16x + 2x2 = 0

Solving
22 + -16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -8x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(11 + -8x + x2)' equal to zero and attempt to solve: Simplifying 11 + -8x + x2 = 0 Solving 11 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -8x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -8x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8x + x2 = 0 + -11 -8x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -8x + x2 = -11 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -11 + 16 Reorder the terms: 16 + -8x + x2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + -8x + x2 = 5 Factor a perfect square on the left side: (x + -4)(x + -4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -4) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + -4 = 2.236067978 Simplifying x + -4 = 2.236067978 Reorder the terms: -4 + x = 2.236067978 Solving -4 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.236067978 + 4 x = 2.236067978 + 4 Combine like terms: 2.236067978 + 4 = 6.236067978 x = 6.236067978 Simplifying x = 6.236067978

Subproblem 2

x + -4 = -2.236067978 Simplifying x + -4 = -2.236067978 Reorder the terms: -4 + x = -2.236067978 Solving -4 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.236067978 + 4 x = -2.236067978 + 4 Combine like terms: -2.236067978 + 4 = 1.763932022 x = 1.763932022 Simplifying x = 1.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.236067978, 1.763932022}

Solution

x = {6.236067978, 1.763932022}

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